If ∠LKJ and ∠GHI are complementary angles, their measures must add up to 90°. So, the angle measure of ∠GHI is 90° - ∠LKJ.
We don't know the measure of ∠LKJ from the given information, so we cannot determine the angle measure of ∠GHI.
Therefore, none of the given options (56°, 146°, 124°, or 66°) are correct.